Strongly Correlated Quantum Systems (SCQ)

Chris Hooley

This course deals mainly with the influence of interactions on the electrons in materials. We begin with a review of second quantisation and the Fermi gas theory of metals, and then progress to Landau’s Fermi liquid theory and the notion of quasiparticles. The effect of impurities on the Fermi liquid (including the Kondo effect) is discussed, and we then move on to consider how the Fermi liquid gives way to other phases as the interactions are increased, concentrating on the Stoner instability and the Mott insulator. We analyse the magnetism in the Mott insulating phase, developing the concept of spin waves. Finally, we make a survey of some experimental data on strongly correlated crystalline solids, giving basic interpretations in terms of the concepts developed in the course.

Chris is a reader at the University of St Andrews. He works on various topics in the theory of strong correlations, including non-Fermi-liquids, highly frustrated magnets, non-equilibrium atomic fluids, and vortex-mediated phase transitions.

Topological Phases of Matter (TOP)

Sam Carr

The well-known Landau theory of phase transitions classifies phases of matter according to broken symmetries and local order parameters, such as solids that break translational symmetry, or magnets that break magnetic rotation symmetry.  It has been long known that there are phases of matter that defy this classification — the quantum Hall state being the most obvious (but by no means only) example.  With the discovery of topological insulators about 10 years ago, interest in this field has exploded, and we now know of many distinct phases of matter with no local order parameter, but instead characterised by a topological invariant.  This short lecture course will focus mostly on non-interacting band theory, and introduce topological invariants, boundary states, and the bulk-boundary correspondence necessary to understand the modern topic of topological insulators.  Other manifestations of topology in modern condensed matter physics will also be exposed, although not discussed in detail.

Sam works on the theory of strongly correlated systems, specialising in low-dimensional systems both in and out of equilibrium. He has worked in groups in the US, Italy and Germany, and since 2013 has been a lecturer at the University of Kent in Canterbury.